Modeling actuarial data using iterated trigonometric distributions

Shahid Mohammad and Kahadawala Cooray

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 16, 5112-5128

Abstract: A new class of trigonometric distribution (TD) is developed iteratively by replacing the random variable of the TD function (or its survival function) with another TD function (or its survival function). The resulting families of distributions produce various density and hazard shapes and a wide variety of tail shapes for the parametric modeling of complex data arising in actuarial science. The basic properties of these distributions are studied and presented. The new TDs successfully model the AON Re Belgian and Danish fire insurance data sets. Risk measures such as value at risk (VaR) and conditional tail expectation (CTE) are computed and compared with their empirical values and other distributions presented in actuarial literature. Also, limited expected values (LEV) for various policy limits are computed to compare with empirical counterparts to emphasize the new TDs’ validity for actuarial predictions.

Date: 2025
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DOI: 10.1080/03610926.2024.2431867

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